Gauss-Bonnet Black Holes in AdS Spaces

TL;DR

This paper investigates the thermodynamics and phase transitions of topological Gauss-Bonnet black holes in Anti-de Sitter spaces, revealing how horizon curvature and spacetime dimension influence their stability and phase structure.

Contribution

It provides a detailed analysis of how Gauss-Bonnet corrections affect black hole thermodynamics across different horizon topologies and dimensions, highlighting new stable phases in five dimensions.

Findings

Black hole thermodynamics depend on horizon curvature and spacetime dimension.

A new stable small black hole phase appears in 5D for certain Gauss-Bonnet coefficients.

Hawking-Page phase transition is absent below a minimal horizon radius.

Abstract

We study thermodynamic properties and phase structures of topological black holes in Einstein theory with a Gauss-Bonnet term and a negative cosmological constant. The event horizon of these topological black holes can be a hypersurface with positive, zero or negative constant curvature. When the horizon is a zero curvature hypersurface, the thermodynamic properties of black holes are completely the same as those of black holes without the Gauss-Bonnet term, although the two black hole solutions are quite different. When the horizon is a negative constant curvature hypersurface, the thermodynamic properties of the Gauss-Bonnet black holes are qualitatively similar to those of black holes without the Gauss-Bonnet term. When the event horizon is a hypersurface with positive constant curvature, we find that the thermodynamic properties and phase structures of black holes drastically depend on the spacetime dimension $d$ and the coefficient of the Gauss-Bonnet term: when $d\ge 6$, the properties of black hole are also qualitatively similar to the case without the Gauss-Bonnet term, but when $d=5$, a new phase of locally stable small black hole occurs under a critical value of the Gauss-Bonnet coefficient, and beyond the critical value, the black holes are always thermodynamically stable. However, the locally stable small black hole is not globally preferred, instead a thermal anti-de Sitter space is globally preferred. We find that there is a minimal horizon radius, below which the Hawking-Page phase transition will not occur since for these black holes the thermal anti de Sitter space is always globally preferred.